CN113836760A - Turbine disk creep fatigue life reliability assessment method - Google Patents
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Abstract
The invention relates to a method for evaluating the creep fatigue life reliability of a turbine disk, which comprises the following steps: s1: establishing a finite element model of the turbine disc, and determining the most dangerous position of the turbine disc through finite element simulation; s2: selecting a random variable according to the multi-source uncertainty factor, sampling the random variable to be used as the input of a finite element model, and obtaining the response output of a finite element; s3: constructing a proxy model for machine learning according to the input of the finite element model and the corresponding finite element response output, and performing sampling simulation on the basis of the proxy model to obtain output data; s4: based on the output data, the reliability of the life was evaluated by using a creep fatigue damage interaction map with a simplified continuous envelope. According to the method for evaluating the creep fatigue life reliability of the turbine disk, the proxy model is constructed through a certain amount of random finite element simulation data, and large-scale sampling simulation is carried out on the basis of the proxy model, so that the finite element simulation times are reduced, the efficiency is improved, and the cost is saved.
Description
Technical Field
The invention relates to the field of creep fatigue reliability evaluation, in particular to a reliability evaluation method of a turbine disk under the interaction of creep fatigue loads.
Background
The turbine disk is a key component of an aircraft engine and bears serious creep fatigue load interaction in a complex service environment, and the creep fatigue interaction becomes a key factor for limiting the service life of the structural component; of more concern are due to a number of sources of uncertainty such as: the dispersion of material properties, the random fluctuation of load, the uncertainty of geometric dimension and the like cause the service life of the turbine disk to present a considerable dispersion characteristic.
In order to consider the service life dispersity caused by the uncertainty factors, conservative design is conventionally performed by using safety factors, but the result of the conservative design is too conservative, so that serious material waste is caused, and the probabilistic reliability analysis method is used for designing and evaluating the reliability service life by quantitatively representing the uncertainty factors in a probability manner and obtaining probability service life distribution by means of finite element simulation coupled sampling technology and using a proper reliability evaluation criterion.
A large number of finite element sampling simulations are required to obtain the probability life distribution, and the calculation of creep deformation and fatigue damage of the finite element simulated turbine disk is extremely time-consuming, so that the cost is obviously huge when ten thousand sampling simulations are carried out by means of random finite elements; in addition, currently, there is no good reliability assessment criterion for creep fatigue damage interaction, which brings a series of difficulties to the reliability assessment of the creep fatigue life of the turbine disk.
Disclosure of Invention
The invention aims to provide a method for evaluating the reliability of the creep fatigue life of a turbine disk.
In order to achieve the above object, the present invention provides a method for evaluating creep fatigue life reliability of a turbine disk, comprising the steps of:
s1: establishing a three-dimensional finite element model of the turbine disc, embedding a creep fatigue constitutive model and a creep fatigue damage model, and determining the most dangerous position of the turbine disc through finite element simulation;
s2: selecting a random variable according to the finite element model of the turbine disc, sampling the random variable to be used as the input of the finite element model and obtaining the finite element response output;
s3: constructing a proxy model for machine learning according to the input of the finite element model and the corresponding finite element response output, and performing sampling simulation for a plurality of times on the basis of the proxy model to obtain a plurality of groups of output data;
s4: based on the output data in step S3, the reliability of the lifetime is evaluated using the creep fatigue damage interaction map with the simplified continuous envelope.
Further, the random variables in step S2 include physical random variables and model random variables.
Further, the physical random variables include rotation speed, density, and elastic modulus.
Further, the model random variables include parameters of a creep damage model and a fatigue damage model.
Further, the parameters of the creep damage model comprise a model constant and a critical failure strain energy density which are fit to the function relationship of the failure strain energy density and the inelastic strain energy density dissipation rate; the parameters of the fatigue damage model include a fatigue strength coefficient, a fatigue ductility coefficient, a fatigue strength index, and a fatigue ductility index.
Further, the outputs in steps S2 and S3 are creep damage and fatigue damage per cycle at the most dangerous position at the steady state.
Further, step S3 further includes:
s31: respectively selecting a support vector regression model and a generalized regression neural network model as candidate agent models, and training and testing the candidate agent models based on the input of a finite element model and the output of finite element response;
s32: and randomly dividing 70% of the input of the finite element model and the finite element response output as a training set and 30% as a test set, comparing the test errors of the support vector regression model and the generalized regression neural network model, and selecting the model with smaller test error as a final agent model.
Further, the agent model in S32 evaluates its test error on the test set as the average absolute percentage error, and satisfies the following relation:
wherein n istestNumber of samples for test set, yiFor each cycle of creep damage and fatigue damage calculated by finite element simulation,
MAPE is the mean absolute percentage error for weekly creep and fatigue damage per cycle predicted by the surrogate model.
Further, step S4 further includes:
s41: calculating, for any given design life, the cumulative creep damage and cumulative fatigue damage of the turbine disk at the time of the cycle reaching the design life based on the sets of output data in step S3;
s42: and performing reliability evaluation on the creep fatigue life of the turbine disk according to the accumulated creep damage and the accumulated fatigue damage by using a creep fatigue damage interaction diagram attached with a simplified continuous envelope curve.
Further, the cumulative creep damage and the cumulative fatigue damage satisfy the following relational expressions:
Dci＝Nd·dci,i＝1,2,...,N
Dfi＝Nd·dfi,i＝1,2,...,N
wherein D isciTo accumulate creep damage, DfiIn order to accumulate fatigue damage, N is the sampling simulation times, and i is the ith sampling simulation.
Further, the simplified continuous envelope is:
where n is the power exponent of the simplified continuous envelope.
Further, the probability of failure of a turbine disk at a given design life satisfies the following relationship:
wherein F is failure factor, failure time is set to 1, safety time is set to 0, P isfIn order to be a probability of failure,
reliability at a given design life is R-1-Pf(Nd)。
According to the method for evaluating the reliability of the creep fatigue life of the turbine disk, firstly, a proxy model is built through a certain amount of random finite element simulation data, then large-scale sampling simulation is carried out based on the proxy model so as to obtain creep damage and fatigue damage distribution, and reliability evaluation is carried out based on a creep fatigue interaction diagram attached with a continuous envelope curve, so that a more safe and conservative reliability evaluation result is obtained. The invention can reduce the finite element simulation times by carrying out large-scale sampling simulation based on the proxy model, thereby improving the efficiency and saving the cost.
Drawings
FIG. 1 is a flow chart of a method for evaluating creep fatigue life reliability of a turbine disk according to an embodiment of the present invention;
FIGS. 2A-2C are graphs of final proxy model-based sampling results, where FIG. 2A is a weekly probability distribution of creep damage, FIG. 2B is a weekly probability distribution of fatigue damage, and FIG. 2C is a creep fatigue life probability distribution, according to an embodiment of the present invention;
FIG. 3 is a graph of failure probability versus design life based on load-life interference criteria, strength-damage interference criteria, and the evaluation method of the present invention;
FIG. 4 is a graph comparing design life at 99.85% reliability based on the load-life interference criterion, the intensity-damage interference criterion, and the evaluation method of the present invention.
Detailed Description
The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
As shown in FIG. 1, the invention provides a method for evaluating the creep fatigue life reliability of a turbine disk, which comprises the following steps:
s1: establishing a three-dimensional finite element model according to the structural characteristics of the turbine disc, embedding a creep fatigue constitutive model and a creep fatigue damage model aiming at the creep fatigue interaction borne by the turbine disc in the actual service process, and determining the most dangerous position of the turbine disc through finite element simulation;
in this embodiment, the ABAQUS software may be used to build a three-dimensional finite element model of the turbine disk, and the code written in Fortran language is used to embed the creep fatigue constitutive model and the damage model through a user sub-program interface (UMAT).
The creep fatigue constitutive equation comprises a cyclic elastoplasticity constitutive model for describing fatigue behavior, and a strain strengthening constitutive model for describing creep behavior, and can adopt the constitutive equation disclosed in the patent application with the application number of CN 202010289799.6; the creep fatigue damage model can adopt a multi-axis creep fatigue damage model provided in the literature [ Wang RZ, et al, Multi-axial crop-fatigue life prediction knowledge-dependent data evaluation: A new numerical procedure and experimental evaluation [ J ]. Journal of the Mechanics and Physics of Solids,2019,131:313-316], and can accurately predict the creep fatigue life of a sample containing holes (in a multi-axis stress state), and the test precision is within 1.5 times of an error band.
Considering the symmetric structure of the turbine disk, in order to reduce the calculation cost as much as possible, in the present embodiment, only 1/72 structures of the turbine disk are constructed for finite element simulation.
In this embodiment, a GH4169 alloy is used as a material of a turbine disk, creep fatigue deformation behavior and damage size of the turbine disk in a high-temperature service state are described according to a constitutive equation and multi-axis creep fatigue damage model parameters disclosed in the above patent documents, the damage model parameters, the material parameters, and rotation speed parameters of the turbine disk in normal service are used as deterministic inputs to perform finite element simulation, and a most dangerous position is determined according to the total creep fatigue damage size.
S2: selecting corresponding random variables in consideration of multi-source uncertainty factors, sampling the selected random variables to be used as input of a finite element model of the turbine disk, and obtaining finite element response output;
s2 further includes the steps of:
s21: selecting random variables aiming at a finite element model of the turbine disc according to actual multisource uncertainty factors, and totally dividing the random variables into physical random variables and model random variables;
wherein, the physical random variables comprise rotating speed, density and elastic modulus, which are respectively expressed as: ω, ρ, E; the model random variables include parameters of a creep damage model and a fatigue damage model, in this embodiment, the damage model used is a strain energy density exhaustion model, and the model random variables are respectively expressed as:
n1,wf,crit,σ'f,ε'f,b0,c0wherein, in the step (A),
n1,wf,critis a creep damage model parameter, σ'f,ε'f,b0,c0Are fatigue damage model parameters.
And n1Fitting a model constant, w, of the relationship between the failure strain energy density and the inelastic strain energy density dissipation ratiof,critCritical failure strain energy density; sigma'f，ε'fRespectively, fatigue strength coefficient and fatigue ductility coefficient, b0，c0The fatigue strength index and the fatigue ductility index are respectively. The specific distribution of random variables is shown in table 1 below.
Table 1: multiple source uncertainty input
It should be noted that, only the more important representative variables are listed in table 1, not all the random variables, and other random variables may be selected according to actually considered uncertainty factors, which is not limited by the present invention.
S22: according to the selected random variable, performing multiple groups of sampling by utilizing a Latin hypercube sampling technology to serve as input of a finite element model of the turbine disk and obtain finite element response output;
wherein the finite element response output refers to creep damage d per cycle at the most dangerous locationcAnd fatigue damage df；
In this embodiment, 50 sets of data were obtained by sampling, i.e., performing 50 finite element simulations. The number of groups of samples can be selected according to actual needs, and in other embodiments, more than or less than 50 groups can be selected.
S3: constructing a proxy model for machine learning according to the input of the finite element model and the finite element response output, and performing sampling simulation for a plurality of times on the basis of the proxy model to obtain a plurality of groups of output data;
s3 further includes the steps of:
s31: respectively selecting a support vector regression model (SVR) and a Generalized Regression Neural Network (GRNN) model as candidate agent models, and training and testing the candidate agent models based on the input of a finite element model and the output of a finite element response;
wherein, the input of the finite element model is 50 groups of physical random variables and model random variables obtained by sampling by a Latin hypercube sampling technology;
s32: randomly dividing the input of the finite element model and the output of the finite element response into 70% as a training set and 30% as a testing set, and determining the optimal hyperparameter (penalty parameter C and kernel function parameter g) of the SVR by adopting a grid search algorithm aiming at the SVR; determining the optimal hyper-parameter of GRNN, namely a smoothing factor s, by adopting a trial and error method aiming at the GRNN; selecting a final agent model according to the optimal hyper-parameter;
specifically, in the present embodiment, 70% of 50 sets of input and output data, i.e., 35 sets, are used as the training set, and the remaining 15 sets are used as the test set.
The test Error of the surrogate model on the test set was evaluated as a Mean Absolute Percentage Error (MAPE) index, which can be expressed as:
wherein n istestNumber of samples for test set, yiFor each cycle of creep damage and fatigue damage calculated by finite element simulation,
creep and fatigue damage per cycle predicted by the surrogate model; the smaller the MAPE index is, the better the prediction effect is, and the minimum hyperparameter of the MAPE is the optimal hyperparameter;
the best hyperparameters of SVR and GRNN determined from MAPE indicators are shown in Table 2 below.
TABLE 2 proxy model optimal hyper-parameters
Under the optimal hyper-parameter, the MAPE of the SVR is 0.0219 and is less than 0.13 of GRNN, which indicates that the test effect of the SVR is better, so that the SVR model is selected as a final agent model.
S33: performing a number of sampling simulations on the final proxy model based on the selected random variables and obtaining damage outputs d at a number of sets of hazardous locationsc，dfCalculating probability life distribution based on a linear accumulated damage criterion;
the number of sampling simulation can be selected according to actual requirements, and in the embodiment, the number of sampling simulation is 104。
Creep-fatigue life N calculated based on linear damage accumulation criterioncfCan be expressed as:
and finally, the calculation result is shown in fig. 2A-2C, and it can be seen that the creep fatigue life obtained by calculation presents lognormal distribution, and is fit with the probability fatigue life distribution form of the current mainstream, which shows that the sampling simulation result based on the final proxy model is reasonable.
S4: based on the output data obtained from the proxy model, reliability evaluation of the lifetime was performed using a simplified interaction diagram accompanied by continuous envelope creep fatigue damage.
S4 further includes the steps of:
s41: based on several groups obtained (e.g. 10)4Group) injury d at dangerous siteci，dfiFor any given design lifetime NdCalculating cumulative creep loss of the turbine disk at the time of the cycle reaching the corresponding design lifeInjury DciAnd accumulated fatigue damage DfiIt can be expressed as:
Dci＝Nd·dci,i＝1,2,...,N
Dfi＝Nd·dfi,i＝1,2,...,N
wherein, N is the sampling simulation times, and i is the ith sampling simulation. In the present embodiment, N is 104。
S42: and according to the accumulated creep damage and the accumulated fatigue damage, utilizing a creep fatigue damage interaction diagram with a simplified continuous envelope curve to carry out reliability evaluation on the creep fatigue life of the turbine disk, wherein the simplified continuous envelope curve is as follows:
where n is the power exponent of the continuous envelope. Document [ Wang RZ, et al.A modified strand energy development model for crop-factor life prediction [ J].International Journal of Fatigue,2016,90:12-22]Note that when the continuous envelope passes through the (0.3 ) interaction point and n is determined to be 0.576, the continuous envelope can give a more accurate failure estimation result, and therefore, in this embodiment, the envelope at this time is adopted:
subsequent reliability evaluations are performed.
The extreme state function of the creep fatigue damage interaction diagram with the simplified continuous envelope can be expressed as:
the probability of failure of a turbine disk at a given design life can be expressed as:
wherein F is failure factor, failure time is set to 1, safety time is set to 0, P isfFor failure probability, N is the number of times of Latin hypercube sampling, and the reliability at the given design life is R-1-Pf(Nd)。
To illustrate the beneficial effects of the evaluation method of the present invention, the results obtained by the load-life interference criterion and the intensity-damage interference criterion, on which the data used by the method is still 10 obtained from the surrogate model, are compared with the results of the present invention4And (4) setting cycle-to-cycle creep and fatigue damage at dangerous positions.
The evaluation method of the creep fatigue life by the load-life interference criterion and the strength-damage interference criterion is as follows:
the probability of failure at a given design life can be calculated from the load-life interference criteria, and its extreme state equation can be expressed as:
G(Nd)＝Ncf-Nd
wherein N iscfFor the resulting probability lifetime, NdFor a given design life, when G (N)d)<When 0, the system is invalid, otherwise, the system is safe;
reliability evaluation can also be performed according to the intensity-damage interference criterion, and the failure probability at a given design life is calculated, and the extreme state equation can be expressed as:
G(Nd)＝Dcri-D(Nd)，G(Nd)<0 fails, otherwise it is safe;
wherein D iscriCritical damage, D (N)d) To account for the cumulative total damage over a cycle to a given design life, it can be expressed as:
D(Nd)＝(dc+df)·Nd
the expression for critical damage is:
wherein N iscfIn order to provide creep-fatigue life,
the average experimental life under the working condition;
under the deterministic framework, it is generally considered that when the accumulated damage reaches 1 material failure, but when many random factors are considered, the critical damage also has randomness, and through statistically accumulating creep fatigue test data of 16 different load conditions, the distribution of the critical damage at this time is obtained as follows: dcri～N(1,0.14962) The critical damage is a normal distribution with 1 as the mean value 0.1496 as the standard deviation. Wherein, the fatigue test data of different load working conditions are shown in the following table 3.
TABLE 3 creep fatigue test data of GH4169 alloy under different working conditions
Based on the load-life interference criterion, the strength-damage interference criterion and the relationship between the failure probability obtained by the evaluation method of the present invention and the design life as shown in fig. 3, it can be seen that the failure probability obtained by the evaluation method of the present invention is the largest under the same design life, i.e. the turbine disk is considered to be more likely to fail under the design life, and therefore, the evaluation method of the present invention is the most conservative and safe.
In addition, engineering generally requires a design life at a given reliability, and the corresponding design life at a given failure probability can be obtained from fig. 3, for example, when the reliability is 99.85%, the failure probability is 0.15%, and the design life corresponding to 0.15% failure probability in three methods can be obtained from fig. 3, and the result is shown in fig. 4. As can be seen from fig. 4, the load-life interference criterion, the strength-damage interference criterion, and the design lives corresponding to the evaluation method of the present invention are respectively 410, 330, and 285 weeks, and the design life corresponding to the evaluation method of the present invention is the smallest, which indicates that the evaluation method of the present invention can achieve a more safe and conservative reliability evaluation result.
According to the method for evaluating the reliability of the creep fatigue life of the turbine disk, provided by the embodiment of the invention, a proxy model is constructed through a certain amount of random finite element simulation data, large-scale sampling simulation is carried out on the basis of the proxy model so as to obtain the distribution of creep damage and fatigue damage, and the reliability evaluation is carried out on the basis of a creep fatigue interaction diagram attached with a continuous envelope curve, so that a more safe and conservative reliability evaluation result is obtained; the finite element simulation times can be reduced by carrying out large-scale sampling simulation based on the proxy model, so that the efficiency is improved, and the cost is saved.
The above embodiments are merely preferred embodiments of the present invention, which are not intended to limit the scope of the present invention, and various changes may be made in the above embodiments of the present invention. All simple and equivalent changes and modifications made according to the claims and the content of the specification of the present application fall within the scope of the claims of the present patent application. The invention has not been described in detail in order to avoid obscuring the invention.
Claims (12)
1. A method for evaluating the creep fatigue life reliability of a turbine disk is characterized by comprising the following steps:
s1: establishing a three-dimensional finite element model of the turbine disc, embedding a creep fatigue constitutive model and a creep fatigue damage model, and determining the most dangerous position of the turbine disc through finite element simulation;
s2: selecting a random variable according to the finite element model of the turbine disc, sampling the random variable to be used as the input of the finite element model and obtaining the finite element response output;
s3: constructing a proxy model for machine learning according to the input of the finite element model and the corresponding finite element response output, and performing sampling simulation for a plurality of times on the basis of the proxy model to obtain a plurality of groups of output data;
s4: based on the output data in step S3, the reliability of the lifetime is evaluated using the creep fatigue damage interaction map with the simplified continuous envelope.
2. The method for estimating creep fatigue life reliability of a turbine disk according to claim 1, wherein the random variables in step S2 include physical random variables and model random variables.
3. The method of claim 2, wherein the physical random variables include rotational speed, density, modulus of elasticity.
4. The method of claim 2, wherein the model random variables include parameters of a creep damage model and a fatigue damage model.
5. The turbine disk creep fatigue life reliability assessment method of claim 4, wherein the parameters of the creep damage model comprise a model constant and a critical failure strain energy density fitted with a functional relationship of failure strain energy density and inelastic strain energy density dissipation ratio; the parameters of the fatigue damage model include a fatigue strength coefficient, a fatigue ductility coefficient, a fatigue strength index, and a fatigue ductility index.
6. The method of claim 1, wherein the outputs of steps S2 and S3 are creep damage and fatigue damage per cycle at the most dangerous position at steady state.
7. The method for evaluating reliability of creep fatigue life of a turbine disk according to claim 1, wherein the step S3 further comprises:
s31: respectively selecting a support vector regression model and a generalized regression neural network model as candidate agent models, and training and testing the candidate agent models based on the input of a finite element model and the output of finite element response;
s32: and randomly dividing 70% of the input of the finite element model and the finite element response output as a training set and 30% as a test set, comparing the test errors of the support vector regression model and the generalized regression neural network model, and selecting the model with smaller test error as a final agent model.
8. The method of claim 7, wherein the agent model in S32 evaluates its test error on the test set as a mean absolute percentage error, satisfying the following relationship:
wherein n istestNumber of samples for test set, yiFor each cycle of creep damage and fatigue damage calculated by finite element simulation,
MAPE is the mean absolute percentage error for weekly creep and fatigue damage per cycle predicted by the surrogate model.
9. The method for evaluating reliability of creep fatigue life of a turbine disk according to claim 1, wherein the step S4 further comprises:
s41: calculating, for any given design life, the cumulative creep damage and cumulative fatigue damage of the turbine disk at the time of the cycle reaching the design life based on the sets of output data in step S3;
s42: and performing reliability evaluation on the creep fatigue life of the turbine disk according to the accumulated creep damage and the accumulated fatigue damage by using a creep fatigue damage interaction diagram attached with a simplified continuous envelope curve.
10. The turbine disk creep fatigue life reliability evaluation method of claim 9, wherein the accumulated creep damage and the accumulated fatigue damage satisfy the following relation:
Dci＝Nd·dci,i＝1,2,...,N
Dfi＝Nd·dfi,i＝1,2,...,N
wherein D isciTo accumulate creep damage, DfiIn order to accumulate fatigue damage, N is the sampling simulation times, and i is the ith sampling simulation.
11. The method of claim 9, wherein the simplified continuous envelope is:
where n is the power exponent of the simplified continuous envelope.
12. The turbine disk creep fatigue life reliability assessment method of claim 11, wherein the probability of failure of a turbine disk at a given design life satisfies the following relation:
wherein F is failure factor, failure time is set to 1, safety time is set to 0, P isfIn order to be a probability of failure,
reliability at a given design life is R-1-Pf(Nd)。
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